Open AccessConnected domination game: Predomination, Staller-start game, and lexicographic products
Author(s) -
Vesna Iršič
Publication year - 2022
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm190206002i
Subject(s) - lexicographical order , mathematics , mathematical economics , vertex (graph theory) , relation (database) , example of a game without a value , combinatorics , game theory , sequential game , combinatorial game theory , graph , computer science , database
The connected domination game was introduced in 2019 by Borowiecki, Fiedorowicz and Sidorowicz as another variation of the domination game. We answer a problem from their paper regarding the relation between the number of moves in a game where Dominator/Staller starts the game. Additionally, we study the relation to the diameter and present graphs with small game connected domination number. We also determine the value on the lexicographic products, and consider the effect of predomination of a vertex.